Speaker
Description
We study degenerating families of hyperbolic dynamics over complex projective
surfaces by means of the theory of hybrid spaces by Boucksom, Favre, and
Jonsson. For an analytic family of hyperbolic automorphisms
$\{f_t\colon X_t\to X_t\}_{t\in\mathbb{D}^*}$ over projective surfaces $X_t$
that is possibly meromorphically degenerating at the origin, we consider the
family of invariant measures $\{\eta_t\}$ on $X_t$ constructed by Cantat.
The family $f_t$ induces a hyperbolic automorphism
$f^{\mathrm{an}}_{\mathbb{C}((t))}\colon
X^{\mathrm{an}}_{\mathbb{C}((t))}\to X^{\mathrm{an}}_{\mathbb{C}((t))}$
over the induced non-archimedean projective surface, where we also have a
measure $\eta_0$ by Filip. Our main theorem states the weak convergence of
$\{\eta_t\}$ to $\eta_0$ as $t\to0$ over the induced so-called hybrid space.